(*                          Ren-Cang Li, June 1, 1996
                            na.rcli@na-net.ornl.gov   *)

<<ReduceH

(* Possible Brackets *)
cmt[1] =Expand[Cmt[X,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[2] =Expand[Cmt[Y,Cmt[X,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[3] =Expand[Cmt[Y,Cmt[Y,Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[4] =Expand[Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]]];
cmt[5] =Expand[Cmt[Y,Cmt[Y,Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]]];

(* Results: The number of independent brackets:  3.
            The independent brackets are:
                cmt[1], cmt[2], cmt[3].
   Relations:

            cmt[2]-2 cmt[3]+ cmt[4] = 0
            cmt[2]-2 cmt[3]+ cmt[5] = 0  *)

NumBrackets=5;
(* Do[{Print[cmt[i]];Pause[5]},{i,NumBrackets}]; *)

(* The maximum possible length of these vectors *)
MaxL=7!/(2! 5!);

<<ReduceT
